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On the probability of generating a monolithic group

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Date
01/06/2014
Author
Detomi, Eloisa
Lucchini, Andrea
Roney-Dougal, Colva Mary
Funder
EPSRC
Grant ID
EP/I03582X/1
Keywords
Finite group theory
Random generation of finite groups
Finite simple groups
Crown-based power
QA Mathematics
BDC
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Abstract
A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2-generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information about PL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.
Citation
Detomi , E , Lucchini , A & Roney-Dougal , C M 2014 , ' On the probability of generating a monolithic group ' , Journal of Algebra , vol. 407 , pp. 413-433 . https://doi.org/10.1016/j.jalgebra.2014.03.010
Publication
Journal of Algebra
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.jalgebra.2014.03.010
ISSN
0021-8693
Type
Journal article
Rights
Copyright 2014, the authors. This is an open access article under the CC-BY license. http://creativecommons.org/licenses/by/3.0/
Description
This research was supported through EPSRC grant EP/I03582X/1. The APC was paid through RCUK open access block grant funds.
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/4626

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